关于超球面的特征

On the Characterizations of Hyperspheres

讨论了En+1中的超球面的特征,得到了En+1具有正交曲率线网的超曲面M是超球面部分的条件;然后推广了A.vec的一个定理,得到了E5具有正交曲率线网的超曲面M是超球面部分的条件。

This paper first discuss the characteristics of the hyperspheres in E^n＋1 ,we obtained conditions that the Hypersurface with orthogonal system of lines of curvature in E^n＋1 is Hyperspheres; and then generalize one theorem of S vecs, we obtained conditions that the Hypersurface with orthogonal system of lines of curvature in E^5 is Hyperspheres.